Order of accuracy of QUICK and related convection-diffusion schemes
type: Item
instance of: scholarly article
title: Order of accuracy of QUICK and related convection-diffusion schemes
zbMATH Open document ID: 0846.65038
DOI: 10.1016/0307-904X(95)00084-W
author: B. P. Leonnard
published in: Applied Mathematical Modelling
publication date: 1996-09-26T00:00:00Z
review text: This paper is a contribution made in order to attempt to clarify some of the misunderstandings that have arisen in the controversy concerning the formal accuracy of the QUICK scheme in computational fluid dynamics. For definiteness, the author considers the equation \[ {d\phi\over dx}= {1\over \text{Pe}} {d^2\phi\over dx^2}+ S(x), \] where \(\text{Pe}\) \((> 0)\) is the Péclet number. One particular deduction made is that the original QUICK scheme and the SPUDS scheme are both third order; however the QUICK finite volume convection operator is 33\% more accurate than the single point implementation of SPUDS. The analysis is supported by numerical studies and examples and an appendix is given in which the relationship between the truncation error and the discretization error is examined.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 76M20
Mathematics Subject Classification ID: 65L12
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 34B05
zbMATH DE Number: 854983
zbMATH Keywords: QUICK scheme
zbMATH Keywords: computational fluid dynamics
zbMATH Keywords: SPUDS scheme
zbMATH Keywords: truncation error
zbMATH Keywords: discretization error
reviewed by: Brian L. Burrows
MaRDI profile type: Publication
cites work: A stable and accurate convective modelling procedure based on quadratic upstream interpolation
cites work: Comparison of truncation error of finite-difference and finite-volume formulations of convection terms
cites work: Equivalent versions of the quick scheme for finite-difference and finite-volume numerical methods
cites work: A Taylor-series approach to numerical accuracy and a third-order scheme for strong convective flows
cites work: Q3999651
description: scientific article; zbMATH DE number 854983